References
Carayol, H.: Sur les représentations l-adiques associées aux formes modulaires de Hilbert. Ann. Sci. Éc. Norm. Supér., IV. Sér. 19, 409–468 (1986)
Carayol, H.: Formes modulaires et représentations galoisiennes à valeurs dans un anneau local complet. p-adic monodromy and the Birch and Swinnerton-Dyer conjecture (Boston, MA, 1991), Contemp. Math., vol. 165, pp. 213–237. Providence, RI: Am. Math. Soc. 1994
Darmon, H., Diamond, F., Taylor, R.: Fermat’s last theorem. Elliptic curves, modular forms & Fermat’s last theorem (Hong Kong, 1993), pp. 2–140. Cambridge, MA: Internat. Press 1997
Diamond, F.: On congruence modules associated to Λ-adic forms. Compos. Math. 71, 49–83 (1989)
Diamond, F.: The refined conjecture of Serre. Elliptic curves, modular forms, & Fermat’s last theorem (Hong Kong, 1993). Ser. Number Theory, I, pp. 22–37. Cambridge, MA: Internat. Press 1995
Diamond, F.: On deformation rings and Hecke rings. Ann. Math. (2) 144, 137–166 (1996)
Diamond, F., Ribet, K.A.: l-adic modular deformations and Wiles’s “main conjecture”. Modular forms and Fermat’s last theorem (Boston, MA, 1995), pp. 357–371. New York: Springer 1997
Diamond, F., Taylor, R.: Nonoptimal levels of mod l modular representations. Invent. Math. 115, 435–462 (1994)
Diamond, F., Taylor, R.: Lifting modular mod l representations. Duke Math. J. 74, 253–269 (1994)
Greenberg, R.: Iwasawa theory for p-adic representations. Algebraic number theory, Adv. Stud. Pure Math., vol. 17, pp. 97–137. Boston, MA: Academic Press 1989
Greenberg, R.: Iwasawa theory for motives. In L-functions and arithmetic (Durham, 1989), pp. 211–233. Cambridge: Cambridge Univ. Press 1991
Greenberg, R.: Iwasawa theory and p-adic deformations of motives. Motives (Seattle, WA, 1991). Proc. Symp. Pure Math., vol. 55, pp. 193–223. Providence, RI: Am. Math. Soc. 1994
Greenberg, R.: Iwasawa theory for elliptic curves. Arithmetic theory of elliptic curves (Cetraro, 1997). Lect. Notes Math., vol. 1716, pp. 51–144. Berlin: Springer 1999
Greenberg, R., Stevens, G.: p-adic L-functions and p-adic periods of modular forms. Invent. Math. 111, 407–447 (1993)
Greenberg, R., Vatsal, V.: On the Iwasawa invariants of elliptic curves. Invent. Math. 142, 17–63 (2000)
Gross, B.: A tameness criterion for Galois representations associated to modular forms (mod p). Duke Math. J. 61, 445–517 (1990)
Hida, H.: Galois representations into GL2(Z p [[X]]) attached to ordinary cusp forms. Invent. Math. 85, 545–613 (1986)
Hida, H.: Iwasawa modules attached to congruences of cusp forms. Ann. Sci. Éc. Norm. Supér., IV. Sér. 19, 231–273 (1986)
Hida, H.: Modules of congruence of Hecke algebras and L-functions associated with cusp forms. Am. J. Math. 110, 323–382 (1988)
Kato, K.: p-adic Hodge theory and values of zeta functions of modular forms. Cohomologies p-adiques et applications arithmétiques. III. Astérisque 295, 117–290 (2004)
Katz, N.: Higher congruences between modular forms. Ann. Math. (2) 101, 332–367 (1975)
Kitigawa, K.: On standard p-adic L-functions of families of elliptic curves. In: p-adic monodromy and the Birch and Swinnerton-Dyer conjecture (Boston, MA, 1991). Contemp. Math., vol. 165, pp. 81–110. Providence, RI: Am. Math. Soc. 1994
Livné, R.: On the conductors of mod l Galois representations coming from modular forms. J. Number Theory 31, 133–141 (1989)
Matsumura, H.: Commutative ring theory, second edn. Cambridge Studies in Advanced Mathematics, vol. 8. Translated from the Japanese by M. Reid. Cambridge: Cambridge University Press 1989
Mazur, B.: On the arithmetic of special values of L-functions. Invent. Math. 55, 207–240 (1979)
Mazur, B.: Euler systems in arithmetic geometry. Notes from a course at Harvard University (1998), available at http://www.math.amherst.edu/∼taweston
Mazur, B.: The theme of p-adic variation. Mathematics: frontiers and perspectives, pp. 433–459. Providence, RI: Am. Math. Soc. 2000
Mazur, B.: Two-variable p-adic L-functions. Unpublished notes
Mazur, B.: An introduction to the deformation theory of Galois representations. In: Modular forms and Fermat’s last theorem (Boston, MA, 1995), pp. 243–311. New York: Springer 1997
Ochiai, T.: On the two-variable Iwasawa main conjecture for Hida deformations. In preparation
Panchishkin, A.: Two-variable p-adic L-functions attached to eigenfamilies of positive slope. Invent. Math. 154, 551–615 (2003)
Stein, W.: The modular forms explorer. http://modular.fas.harvard.edu/mfd/mfe/
Stevens, G.: Families of overconvergent modular symbols. Preprint
Taylor, R., Wiles, A.: Ring-theoretic properties of certain Hecke algebras. Ann. Math. (2) 141, 553–572 (1995)
Vatsal, V.: Canonical periods and congruence formulae Duke Math. J. 98, 397–419 (1999)
Weston, T.: Iwasawa invariants of Galois deformations. Manuscr. Math. 118, 161–180 (2005)
Wiles, A.: Modular elliptic curves and Fermat’s last theorem. Ann. Math. (2) 141, 443–551 (1995)
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Emerton, M., Pollack, R. & Weston, T. Variation of Iwasawa invariants in Hida families. Invent. math. 163, 523–580 (2006). https://doi.org/10.1007/s00222-005-0467-7
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DOI: https://doi.org/10.1007/s00222-005-0467-7